the gravitation example of F=mg is actually quite useful, because we know that newton's cosmology does not have infinite precision at all, but is rather governed by error relating to what we call the n-body problem. in a newtonian approach to this problem, however deprecated, we need to work in the effects of perturbations from the sun, jupiter and all of the other planetary bodies in order to come up with a perfect orbit, which is not spherical or elliptical at all but, rather, a bumpy and chaotic ride through extreme turbulence.
the point i want to get across is this - in the context of newton's theory, we don't consider this to be "randomness". it's a very hard problem, certainly - unsolvable, in fact. the best we can do is make guesses using differential equations. however, if we didn't understand gravity, we could model the problem using a statistical analysis, and replace the physics that we know exists and call gravity with randomness. and, you know what? we'd get something that's startlingly accurate, if we did that.
just think that through a bit.